Properties

Label 21.7.b.a.8.8
Level $21$
Weight $7$
Character 21.8
Analytic conductor $4.831$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [21,7,Mod(8,21)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(21, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("21.8");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 21.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.83113575602\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 642x^{10} + 155265x^{8} + 17813036x^{6} + 1003321428x^{4} + 26369892864x^{2} + 256461520896 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{8}\cdot 7^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 8.8
Root \(5.92187i\) of defining polynomial
Character \(\chi\) \(=\) 21.8
Dual form 21.7.b.a.8.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+5.92187i q^{2} +(25.5592 - 8.70200i) q^{3} +28.9315 q^{4} -144.537i q^{5} +(51.5321 + 151.359i) q^{6} +129.642 q^{7} +550.328i q^{8} +(577.550 - 444.833i) q^{9} +O(q^{10})\) \(q+5.92187i q^{2} +(25.5592 - 8.70200i) q^{3} +28.9315 q^{4} -144.537i q^{5} +(51.5321 + 151.359i) q^{6} +129.642 q^{7} +550.328i q^{8} +(577.550 - 444.833i) q^{9} +855.929 q^{10} +1762.28i q^{11} +(739.466 - 251.762i) q^{12} -1258.93 q^{13} +767.722i q^{14} +(-1257.76 - 3694.26i) q^{15} -1407.36 q^{16} -6025.19i q^{17} +(2634.24 + 3420.18i) q^{18} -9374.79 q^{19} -4181.67i q^{20} +(3313.55 - 1128.14i) q^{21} -10436.0 q^{22} +15380.6i q^{23} +(4788.95 + 14066.0i) q^{24} -5265.94 q^{25} -7455.20i q^{26} +(10890.8 - 16395.4i) q^{27} +3750.73 q^{28} -17060.6i q^{29} +(21876.9 - 7448.29i) q^{30} -20504.9 q^{31} +26886.8i q^{32} +(15335.3 + 45042.5i) q^{33} +35680.4 q^{34} -18738.0i q^{35} +(16709.4 - 12869.7i) q^{36} +8468.56 q^{37} -55516.3i q^{38} +(-32177.2 + 10955.2i) q^{39} +79542.7 q^{40} +58841.0i q^{41} +(6680.72 + 19622.4i) q^{42} -135972. q^{43} +50985.2i q^{44} +(-64294.8 - 83477.4i) q^{45} -91082.1 q^{46} +28061.3i q^{47} +(-35971.0 + 12246.8i) q^{48} +16807.0 q^{49} -31184.2i q^{50} +(-52431.2 - 153999. i) q^{51} -36422.6 q^{52} -125789. i q^{53} +(97091.7 + 64494.0i) q^{54} +254714. q^{55} +71345.5i q^{56} +(-239612. + 81579.4i) q^{57} +101031. q^{58} +181093. i q^{59} +(-36388.9 - 106880. i) q^{60} +300687. q^{61} -121427. i q^{62} +(74874.7 - 57669.0i) q^{63} -249291. q^{64} +181961. i q^{65} +(-266736. + 90813.8i) q^{66} +314063. q^{67} -174318. i q^{68} +(133842. + 393118. i) q^{69} +110964. q^{70} -438176. i q^{71} +(244804. + 317842. i) q^{72} +49885.6 q^{73} +50149.7i q^{74} +(-134593. + 45824.2i) q^{75} -271226. q^{76} +228465. i q^{77} +(-64875.1 - 190549. i) q^{78} +505643. q^{79} +203415. i q^{80} +(135688. - 513827. i) q^{81} -348449. q^{82} +341518. i q^{83} +(95865.8 - 32638.8i) q^{84} -870863. q^{85} -805211. i q^{86} +(-148461. - 436056. i) q^{87} -969830. q^{88} -824180. i q^{89} +(494342. - 380746. i) q^{90} -163210. q^{91} +444984. i q^{92} +(-524090. + 178434. i) q^{93} -166175. q^{94} +1.35500e6i q^{95} +(233969. + 687207. i) q^{96} -142772. q^{97} +99528.9i q^{98} +(783919. + 1.01780e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 52 q^{3} - 516 q^{4} + 350 q^{6} - 644 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 52 q^{3} - 516 q^{4} + 350 q^{6} - 644 q^{9} - 1092 q^{10} - 1726 q^{12} + 384 q^{13} - 632 q^{15} + 5892 q^{16} - 40 q^{18} + 11304 q^{19} - 5488 q^{21} + 15312 q^{22} + 12138 q^{24} - 77292 q^{25} + 114796 q^{27} + 41160 q^{28} - 101908 q^{30} - 9360 q^{31} - 65744 q^{33} - 169008 q^{34} - 195652 q^{36} + 212016 q^{37} + 159544 q^{39} + 196644 q^{40} - 37730 q^{42} + 28080 q^{43} - 4760 q^{45} - 418512 q^{46} + 865742 q^{48} + 201684 q^{49} - 371880 q^{51} - 138300 q^{52} - 254170 q^{54} - 732144 q^{55} - 440624 q^{57} + 1164240 q^{58} + 677660 q^{60} + 926736 q^{61} + 2744 q^{63} - 1380108 q^{64} - 1414588 q^{66} - 223104 q^{67} + 153048 q^{69} - 382788 q^{70} - 540192 q^{72} + 600984 q^{73} + 594716 q^{75} + 604596 q^{76} + 1866140 q^{78} - 276864 q^{79} + 617596 q^{81} + 1138200 q^{82} + 1398754 q^{84} - 3002472 q^{85} - 3372824 q^{87} - 1599048 q^{88} - 788032 q^{90} - 1243032 q^{91} + 408168 q^{93} + 8059296 q^{94} - 1141658 q^{96} + 1621416 q^{97} + 5211904 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.92187i 0.740234i 0.928985 + 0.370117i \(0.120682\pi\)
−0.928985 + 0.370117i \(0.879318\pi\)
\(3\) 25.5592 8.70200i 0.946639 0.322296i
\(4\) 28.9315 0.452054
\(5\) 144.537i 1.15630i −0.815932 0.578148i \(-0.803776\pi\)
0.815932 0.578148i \(-0.196224\pi\)
\(6\) 51.5321 + 151.359i 0.238575 + 0.700734i
\(7\) 129.642 0.377964
\(8\) 550.328i 1.07486i
\(9\) 577.550 444.833i 0.792250 0.610196i
\(10\) 855.929 0.855929
\(11\) 1762.28i 1.32402i 0.749493 + 0.662012i \(0.230297\pi\)
−0.749493 + 0.662012i \(0.769703\pi\)
\(12\) 739.466 251.762i 0.427932 0.145695i
\(13\) −1258.93 −0.573021 −0.286510 0.958077i \(-0.592495\pi\)
−0.286510 + 0.958077i \(0.592495\pi\)
\(14\) 767.722i 0.279782i
\(15\) −1257.76 3694.26i −0.372670 1.09459i
\(16\) −1407.36 −0.343593
\(17\) 6025.19i 1.22638i −0.789936 0.613189i \(-0.789886\pi\)
0.789936 0.613189i \(-0.210114\pi\)
\(18\) 2634.24 + 3420.18i 0.451688 + 0.586450i
\(19\) −9374.79 −1.36679 −0.683393 0.730051i \(-0.739496\pi\)
−0.683393 + 0.730051i \(0.739496\pi\)
\(20\) 4181.67i 0.522708i
\(21\) 3313.55 1128.14i 0.357796 0.121817i
\(22\) −10436.0 −0.980087
\(23\) 15380.6i 1.26413i 0.774916 + 0.632064i \(0.217792\pi\)
−0.774916 + 0.632064i \(0.782208\pi\)
\(24\) 4788.95 + 14066.0i 0.346423 + 1.01750i
\(25\) −5265.94 −0.337020
\(26\) 7455.20i 0.424169i
\(27\) 10890.8 16395.4i 0.553311 0.832975i
\(28\) 3750.73 0.170860
\(29\) 17060.6i 0.699520i −0.936839 0.349760i \(-0.886263\pi\)
0.936839 0.349760i \(-0.113737\pi\)
\(30\) 21876.9 7448.29i 0.810256 0.275863i
\(31\) −20504.9 −0.688292 −0.344146 0.938916i \(-0.611832\pi\)
−0.344146 + 0.938916i \(0.611832\pi\)
\(32\) 26886.8i 0.820520i
\(33\) 15335.3 + 45042.5i 0.426728 + 1.25337i
\(34\) 35680.4 0.907806
\(35\) 18738.0i 0.437039i
\(36\) 16709.4 12869.7i 0.358140 0.275842i
\(37\) 8468.56 0.167188 0.0835939 0.996500i \(-0.473360\pi\)
0.0835939 + 0.996500i \(0.473360\pi\)
\(38\) 55516.3i 1.01174i
\(39\) −32177.2 + 10955.2i −0.542444 + 0.184682i
\(40\) 79542.7 1.24286
\(41\) 58841.0i 0.853745i 0.904312 + 0.426873i \(0.140385\pi\)
−0.904312 + 0.426873i \(0.859615\pi\)
\(42\) 6680.72 + 19622.4i 0.0901727 + 0.264853i
\(43\) −135972. −1.71019 −0.855097 0.518468i \(-0.826503\pi\)
−0.855097 + 0.518468i \(0.826503\pi\)
\(44\) 50985.2i 0.598531i
\(45\) −64294.8 83477.4i −0.705567 0.916076i
\(46\) −91082.1 −0.935750
\(47\) 28061.3i 0.270280i 0.990826 + 0.135140i \(0.0431485\pi\)
−0.990826 + 0.135140i \(0.956852\pi\)
\(48\) −35971.0 + 12246.8i −0.325259 + 0.110739i
\(49\) 16807.0 0.142857
\(50\) 31184.2i 0.249474i
\(51\) −52431.2 153999.i −0.395257 1.16094i
\(52\) −36422.6 −0.259036
\(53\) 125789.i 0.844921i −0.906381 0.422460i \(-0.861167\pi\)
0.906381 0.422460i \(-0.138833\pi\)
\(54\) 97091.7 + 64494.0i 0.616596 + 0.409579i
\(55\) 254714. 1.53096
\(56\) 71345.5i 0.406259i
\(57\) −239612. + 81579.4i −1.29385 + 0.440510i
\(58\) 101031. 0.517808
\(59\) 181093.i 0.881751i 0.897568 + 0.440876i \(0.145332\pi\)
−0.897568 + 0.440876i \(0.854668\pi\)
\(60\) −36388.9 106880.i −0.168467 0.494816i
\(61\) 300687. 1.32472 0.662362 0.749184i \(-0.269554\pi\)
0.662362 + 0.749184i \(0.269554\pi\)
\(62\) 121427.i 0.509497i
\(63\) 74874.7 57669.0i 0.299442 0.230633i
\(64\) −249291. −0.950970
\(65\) 181961.i 0.662582i
\(66\) −266736. + 90813.8i −0.927789 + 0.315878i
\(67\) 314063. 1.04422 0.522111 0.852877i \(-0.325145\pi\)
0.522111 + 0.852877i \(0.325145\pi\)
\(68\) 174318.i 0.554389i
\(69\) 133842. + 393118.i 0.407424 + 1.19667i
\(70\) 110964. 0.323511
\(71\) 438176.i 1.22426i −0.790758 0.612129i \(-0.790313\pi\)
0.790758 0.612129i \(-0.209687\pi\)
\(72\) 244804. + 317842.i 0.655875 + 0.851558i
\(73\) 49885.6 0.128235 0.0641175 0.997942i \(-0.479577\pi\)
0.0641175 + 0.997942i \(0.479577\pi\)
\(74\) 50149.7i 0.123758i
\(75\) −134593. + 45824.2i −0.319036 + 0.108620i
\(76\) −271226. −0.617861
\(77\) 228465.i 0.500434i
\(78\) −64875.1 190549.i −0.136708 0.401535i
\(79\) 505643. 1.02556 0.512782 0.858519i \(-0.328615\pi\)
0.512782 + 0.858519i \(0.328615\pi\)
\(80\) 203415.i 0.397295i
\(81\) 135688. 513827.i 0.255321 0.966856i
\(82\) −348449. −0.631971
\(83\) 341518.i 0.597281i 0.954366 + 0.298641i \(0.0965332\pi\)
−0.954366 + 0.298641i \(0.903467\pi\)
\(84\) 95865.8 32638.8i 0.161743 0.0550677i
\(85\) −870863. −1.41806
\(86\) 805211.i 1.26594i
\(87\) −148461. 436056.i −0.225453 0.662192i
\(88\) −969830. −1.42314
\(89\) 824180.i 1.16910i −0.811357 0.584550i \(-0.801271\pi\)
0.811357 0.584550i \(-0.198729\pi\)
\(90\) 494342. 380746.i 0.678110 0.522285i
\(91\) −163210. −0.216582
\(92\) 444984.i 0.571454i
\(93\) −524090. + 178434.i −0.651564 + 0.221834i
\(94\) −166175. −0.200071
\(95\) 1.35500e6i 1.58041i
\(96\) 233969. + 687207.i 0.264451 + 0.776736i
\(97\) −142772. −0.156433 −0.0782167 0.996936i \(-0.524923\pi\)
−0.0782167 + 0.996936i \(0.524923\pi\)
\(98\) 99528.9i 0.105748i
\(99\) 783919. + 1.01780e6i 0.807915 + 1.04896i
\(100\) −152351. −0.152351
\(101\) 656702.i 0.637388i −0.947858 0.318694i \(-0.896756\pi\)
0.947858 0.318694i \(-0.103244\pi\)
\(102\) 911965. 310491.i 0.859365 0.292583i
\(103\) 773197. 0.707585 0.353792 0.935324i \(-0.384892\pi\)
0.353792 + 0.935324i \(0.384892\pi\)
\(104\) 692823.i 0.615917i
\(105\) −163058. 478930.i −0.140856 0.413718i
\(106\) 744908. 0.625439
\(107\) 1.45353e6i 1.18651i 0.805014 + 0.593256i \(0.202158\pi\)
−0.805014 + 0.593256i \(0.797842\pi\)
\(108\) 315087. 474344.i 0.250126 0.376550i
\(109\) −439044. −0.339022 −0.169511 0.985528i \(-0.554219\pi\)
−0.169511 + 0.985528i \(0.554219\pi\)
\(110\) 1.50838e6i 1.13327i
\(111\) 216450. 73693.4i 0.158266 0.0538840i
\(112\) −182452. −0.129866
\(113\) 1.30626e6i 0.905307i −0.891686 0.452653i \(-0.850477\pi\)
0.891686 0.452653i \(-0.149523\pi\)
\(114\) −483102. 1.41895e6i −0.326080 0.957753i
\(115\) 2.22307e6 1.46171
\(116\) 493588.i 0.316221i
\(117\) −727094. + 560012.i −0.453976 + 0.349655i
\(118\) −1.07241e6 −0.652702
\(119\) 781117.i 0.463527i
\(120\) 2.03305e6 692181.i 1.17654 0.400568i
\(121\) −1.33406e6 −0.753040
\(122\) 1.78063e6i 0.980606i
\(123\) 512034. + 1.50393e6i 0.275159 + 0.808188i
\(124\) −593237. −0.311145
\(125\) 1.49727e6i 0.766601i
\(126\) 341508. + 443398.i 0.170722 + 0.221657i
\(127\) 2.38957e6 1.16656 0.583281 0.812270i \(-0.301768\pi\)
0.583281 + 0.812270i \(0.301768\pi\)
\(128\) 244487.i 0.116580i
\(129\) −3.47535e6 + 1.18323e6i −1.61894 + 0.551189i
\(130\) −1.07755e6 −0.490465
\(131\) 2.11936e6i 0.942739i −0.881936 0.471370i \(-0.843760\pi\)
0.881936 0.471370i \(-0.156240\pi\)
\(132\) 443673. + 1.30314e6i 0.192904 + 0.566592i
\(133\) −1.21536e6 −0.516597
\(134\) 1.85984e6i 0.772969i
\(135\) −2.36975e6 1.57413e6i −0.963165 0.639791i
\(136\) 3.31583e6 1.31818
\(137\) 1.08490e6i 0.421919i −0.977495 0.210959i \(-0.932341\pi\)
0.977495 0.210959i \(-0.0676588\pi\)
\(138\) −2.32799e6 + 792597.i −0.885817 + 0.301589i
\(139\) −3.92436e6 −1.46125 −0.730626 0.682778i \(-0.760771\pi\)
−0.730626 + 0.682778i \(0.760771\pi\)
\(140\) 542119.i 0.197565i
\(141\) 244190. + 717226.i 0.0871103 + 0.255858i
\(142\) 2.59482e6 0.906237
\(143\) 2.21858e6i 0.758693i
\(144\) −812820. + 626039.i −0.272212 + 0.209659i
\(145\) −2.46589e6 −0.808852
\(146\) 295416.i 0.0949238i
\(147\) 429574. 146254.i 0.135234 0.0460423i
\(148\) 245008. 0.0755779
\(149\) 2.16645e6i 0.654922i 0.944865 + 0.327461i \(0.106193\pi\)
−0.944865 + 0.327461i \(0.893807\pi\)
\(150\) −271365. 797045.i −0.0804044 0.236161i
\(151\) 4.33862e6 1.26015 0.630073 0.776536i \(-0.283025\pi\)
0.630073 + 0.776536i \(0.283025\pi\)
\(152\) 5.15921e6i 1.46910i
\(153\) −2.68021e6 3.47985e6i −0.748331 0.971598i
\(154\) −1.35294e6 −0.370438
\(155\) 2.96372e6i 0.795869i
\(156\) −930934. + 316949.i −0.245214 + 0.0834865i
\(157\) 5.30473e6 1.37077 0.685384 0.728182i \(-0.259634\pi\)
0.685384 + 0.728182i \(0.259634\pi\)
\(158\) 2.99435e6i 0.759157i
\(159\) −1.09462e6 3.21508e6i −0.272315 0.799835i
\(160\) 3.88614e6 0.948764
\(161\) 1.99397e6i 0.477795i
\(162\) 3.04282e6 + 803527.i 0.715700 + 0.188997i
\(163\) 4.58667e6 1.05910 0.529548 0.848280i \(-0.322362\pi\)
0.529548 + 0.848280i \(0.322362\pi\)
\(164\) 1.70236e6i 0.385939i
\(165\) 6.51030e6 2.21652e6i 1.44927 0.493424i
\(166\) −2.02242e6 −0.442128
\(167\) 6.23982e6i 1.33975i 0.742476 + 0.669873i \(0.233651\pi\)
−0.742476 + 0.669873i \(0.766349\pi\)
\(168\) 620849. + 1.82354e6i 0.130936 + 0.384580i
\(169\) −3.24191e6 −0.671647
\(170\) 5.15714e6i 1.04969i
\(171\) −5.41441e6 + 4.17021e6i −1.08284 + 0.834008i
\(172\) −3.93388e6 −0.773100
\(173\) 8.17326e6i 1.57854i 0.614043 + 0.789272i \(0.289542\pi\)
−0.614043 + 0.789272i \(0.710458\pi\)
\(174\) 2.58227e6 879168.i 0.490177 0.166888i
\(175\) −682686. −0.127382
\(176\) 2.48015e6i 0.454926i
\(177\) 1.57587e6 + 4.62861e6i 0.284185 + 0.834700i
\(178\) 4.88069e6 0.865408
\(179\) 7.10092e6i 1.23810i −0.785352 0.619050i \(-0.787518\pi\)
0.785352 0.619050i \(-0.212482\pi\)
\(180\) −1.86014e6 2.41512e6i −0.318955 0.414116i
\(181\) −6.92233e6 −1.16739 −0.583696 0.811972i \(-0.698394\pi\)
−0.583696 + 0.811972i \(0.698394\pi\)
\(182\) 966506.i 0.160321i
\(183\) 7.68534e6 2.61658e6i 1.25404 0.426954i
\(184\) −8.46440e6 −1.35876
\(185\) 1.22402e6i 0.193319i
\(186\) −1.05666e6 3.10359e6i −0.164209 0.482310i
\(187\) 1.06181e7 1.62375
\(188\) 811855.i 0.122181i
\(189\) 1.41191e6 2.12554e6i 0.209132 0.314835i
\(190\) −8.02415e6 −1.16987
\(191\) 5.17663e6i 0.742929i −0.928447 0.371464i \(-0.878856\pi\)
0.928447 0.371464i \(-0.121144\pi\)
\(192\) −6.37169e6 + 2.16933e6i −0.900225 + 0.306494i
\(193\) −7.99433e6 −1.11201 −0.556007 0.831178i \(-0.687667\pi\)
−0.556007 + 0.831178i \(0.687667\pi\)
\(194\) 845480.i 0.115797i
\(195\) 1.58343e6 + 4.65080e6i 0.213548 + 0.627225i
\(196\) 486251. 0.0645792
\(197\) 3.39988e6i 0.444698i 0.974967 + 0.222349i \(0.0713724\pi\)
−0.974967 + 0.222349i \(0.928628\pi\)
\(198\) −6.02730e6 + 4.64227e6i −0.776474 + 0.598046i
\(199\) −7.26597e6 −0.922007 −0.461004 0.887398i \(-0.652510\pi\)
−0.461004 + 0.887398i \(0.652510\pi\)
\(200\) 2.89799e6i 0.362249i
\(201\) 8.02723e6 2.73298e6i 0.988501 0.336549i
\(202\) 3.88890e6 0.471816
\(203\) 2.21177e6i 0.264394i
\(204\) −1.51691e6 4.45543e6i −0.178678 0.524806i
\(205\) 8.50470e6 0.987182
\(206\) 4.57877e6i 0.523778i
\(207\) 6.84182e6 + 8.88309e6i 0.771366 + 1.00151i
\(208\) 1.77176e6 0.196886
\(209\) 1.65210e7i 1.80966i
\(210\) 2.83616e6 965610.i 0.306248 0.104266i
\(211\) −1.75679e7 −1.87013 −0.935067 0.354471i \(-0.884661\pi\)
−0.935067 + 0.354471i \(0.884661\pi\)
\(212\) 3.63927e6i 0.381950i
\(213\) −3.81300e6 1.11994e7i −0.394574 1.15893i
\(214\) −8.60760e6 −0.878296
\(215\) 1.96530e7i 1.97749i
\(216\) 9.02287e6 + 5.99352e6i 0.895331 + 0.594731i
\(217\) −2.65829e6 −0.260150
\(218\) 2.59996e6i 0.250956i
\(219\) 1.27504e6 434104.i 0.121392 0.0413296i
\(220\) 7.36925e6 0.692078
\(221\) 7.58528e6i 0.702740i
\(222\) 436403. + 1.28179e6i 0.0398868 + 0.117154i
\(223\) 2.19380e6 0.197825 0.0989127 0.995096i \(-0.468464\pi\)
0.0989127 + 0.995096i \(0.468464\pi\)
\(224\) 3.48565e6i 0.310127i
\(225\) −3.04134e6 + 2.34246e6i −0.267004 + 0.205648i
\(226\) 7.73553e6 0.670139
\(227\) 1.20937e7i 1.03391i −0.856014 0.516953i \(-0.827066\pi\)
0.856014 0.516953i \(-0.172934\pi\)
\(228\) −6.93234e6 + 2.36021e6i −0.584891 + 0.199134i
\(229\) 4.36562e6 0.363529 0.181765 0.983342i \(-0.441819\pi\)
0.181765 + 0.983342i \(0.441819\pi\)
\(230\) 1.31647e7i 1.08200i
\(231\) 1.98810e6 + 5.83939e6i 0.161288 + 0.473730i
\(232\) 9.38892e6 0.751885
\(233\) 6.97793e6i 0.551644i 0.961209 + 0.275822i \(0.0889501\pi\)
−0.961209 + 0.275822i \(0.911050\pi\)
\(234\) −3.31632e6 4.30575e6i −0.258827 0.336048i
\(235\) 4.05590e6 0.312524
\(236\) 5.23929e6i 0.398599i
\(237\) 1.29239e7 4.40010e6i 0.970838 0.330535i
\(238\) 4.62567e6 0.343118
\(239\) 1.31069e7i 0.960075i −0.877248 0.480038i \(-0.840623\pi\)
0.877248 0.480038i \(-0.159377\pi\)
\(240\) 1.77012e6 + 5.19914e6i 0.128047 + 0.376095i
\(241\) 5.41621e6 0.386941 0.193470 0.981106i \(-0.438026\pi\)
0.193470 + 0.981106i \(0.438026\pi\)
\(242\) 7.90011e6i 0.557426i
\(243\) −1.00324e6 1.43138e7i −0.0699175 0.997553i
\(244\) 8.69932e6 0.598847
\(245\) 2.42923e6i 0.165185i
\(246\) −8.90608e6 + 3.03220e6i −0.598248 + 0.203682i
\(247\) 1.18022e7 0.783197
\(248\) 1.12844e7i 0.739817i
\(249\) 2.97189e6 + 8.72893e6i 0.192501 + 0.565410i
\(250\) 8.86662e6 0.567464
\(251\) 2.92888e6i 0.185217i 0.995703 + 0.0926083i \(0.0295204\pi\)
−0.995703 + 0.0926083i \(0.970480\pi\)
\(252\) 2.16623e6 1.66845e6i 0.135364 0.104258i
\(253\) −2.71049e7 −1.67374
\(254\) 1.41507e7i 0.863529i
\(255\) −2.22586e7 + 7.57825e6i −1.34239 + 0.457034i
\(256\) −1.74024e7 −1.03727
\(257\) 1.16323e7i 0.685280i −0.939467 0.342640i \(-0.888679\pi\)
0.939467 0.342640i \(-0.111321\pi\)
\(258\) −7.00694e6 2.05806e7i −0.408009 1.19839i
\(259\) 1.09788e6 0.0631911
\(260\) 5.26441e6i 0.299523i
\(261\) −7.58911e6 9.85335e6i −0.426844 0.554195i
\(262\) 1.25506e7 0.697847
\(263\) 2.06892e7i 1.13730i 0.822578 + 0.568652i \(0.192535\pi\)
−0.822578 + 0.568652i \(0.807465\pi\)
\(264\) −2.47881e7 + 8.43946e6i −1.34720 + 0.458673i
\(265\) −1.81812e7 −0.976978
\(266\) 7.19723e6i 0.382402i
\(267\) −7.17201e6 2.10654e7i −0.376797 1.10672i
\(268\) 9.08631e6 0.472045
\(269\) 2.91650e7i 1.49832i 0.662388 + 0.749161i \(0.269543\pi\)
−0.662388 + 0.749161i \(0.730457\pi\)
\(270\) 9.32177e6 1.40333e7i 0.473595 0.712967i
\(271\) −7.38727e6 −0.371173 −0.185586 0.982628i \(-0.559418\pi\)
−0.185586 + 0.982628i \(0.559418\pi\)
\(272\) 8.47960e6i 0.421375i
\(273\) −4.17151e6 + 1.42025e6i −0.205024 + 0.0698034i
\(274\) 6.42465e6 0.312318
\(275\) 9.28004e6i 0.446223i
\(276\) 3.87225e6 + 1.13735e7i 0.184177 + 0.540961i
\(277\) 2.79150e7 1.31340 0.656702 0.754150i \(-0.271951\pi\)
0.656702 + 0.754150i \(0.271951\pi\)
\(278\) 2.32396e7i 1.08167i
\(279\) −1.18426e7 + 9.12126e6i −0.545300 + 0.419993i
\(280\) 1.03121e7 0.469755
\(281\) 9.14595e6i 0.412202i −0.978531 0.206101i \(-0.933922\pi\)
0.978531 0.206101i \(-0.0660775\pi\)
\(282\) −4.24732e6 + 1.44606e6i −0.189395 + 0.0644820i
\(283\) −2.54163e7 −1.12138 −0.560690 0.828026i \(-0.689464\pi\)
−0.560690 + 0.828026i \(0.689464\pi\)
\(284\) 1.26771e7i 0.553431i
\(285\) 1.17912e7 + 3.46329e7i 0.509360 + 1.49608i
\(286\) 1.31381e7 0.561610
\(287\) 7.62825e6i 0.322685i
\(288\) 1.19601e7 + 1.55285e7i 0.500678 + 0.650057i
\(289\) −1.21654e7 −0.504003
\(290\) 1.46027e7i 0.598739i
\(291\) −3.64916e6 + 1.24241e6i −0.148086 + 0.0504179i
\(292\) 1.44326e6 0.0579691
\(293\) 1.38751e7i 0.551611i −0.961213 0.275806i \(-0.911055\pi\)
0.961213 0.275806i \(-0.0889446\pi\)
\(294\) 866100. + 2.54388e6i 0.0340821 + 0.100105i
\(295\) 2.61747e7 1.01957
\(296\) 4.66049e6i 0.179703i
\(297\) 2.88933e7 + 1.91926e7i 1.10288 + 0.732597i
\(298\) −1.28294e7 −0.484796
\(299\) 1.93631e7i 0.724371i
\(300\) −3.89398e6 + 1.32576e6i −0.144222 + 0.0491022i
\(301\) −1.76277e7 −0.646393
\(302\) 2.56927e7i 0.932802i
\(303\) −5.71462e6 1.67848e7i −0.205428 0.603377i
\(304\) 1.31937e7 0.469618
\(305\) 4.34604e7i 1.53177i
\(306\) 2.06072e7 1.58718e7i 0.719210 0.553940i
\(307\) −2.13868e6 −0.0739147 −0.0369573 0.999317i \(-0.511767\pi\)
−0.0369573 + 0.999317i \(0.511767\pi\)
\(308\) 6.60982e6i 0.226223i
\(309\) 1.97623e7 6.72836e6i 0.669827 0.228052i
\(310\) −1.75508e7 −0.589129
\(311\) 2.20443e7i 0.732851i −0.930447 0.366426i \(-0.880581\pi\)
0.930447 0.366426i \(-0.119419\pi\)
\(312\) −6.02894e6 1.77080e7i −0.198508 0.583051i
\(313\) 7.52711e6 0.245468 0.122734 0.992440i \(-0.460834\pi\)
0.122734 + 0.992440i \(0.460834\pi\)
\(314\) 3.14139e7i 1.01469i
\(315\) −8.33530e6 1.08222e7i −0.266679 0.346244i
\(316\) 1.46290e7 0.463610
\(317\) 1.10809e7i 0.347855i 0.984758 + 0.173928i \(0.0556459\pi\)
−0.984758 + 0.173928i \(0.944354\pi\)
\(318\) 1.90393e7 6.48219e6i 0.592065 0.201577i
\(319\) 3.00655e7 0.926181
\(320\) 3.60318e7i 1.09960i
\(321\) 1.26486e7 + 3.71511e7i 0.382408 + 1.12320i
\(322\) −1.18081e7 −0.353680
\(323\) 5.64849e7i 1.67620i
\(324\) 3.92565e6 1.48658e7i 0.115419 0.437071i
\(325\) 6.62943e6 0.193119
\(326\) 2.71617e7i 0.783978i
\(327\) −1.12216e7 + 3.82056e6i −0.320932 + 0.109266i
\(328\) −3.23818e7 −0.917656
\(329\) 3.63792e6i 0.102156i
\(330\) 1.31260e7 + 3.85532e7i 0.365249 + 1.07280i
\(331\) −3.15332e7 −0.869528 −0.434764 0.900544i \(-0.643168\pi\)
−0.434764 + 0.900544i \(0.643168\pi\)
\(332\) 9.88060e6i 0.270003i
\(333\) 4.89102e6 3.76710e6i 0.132455 0.102017i
\(334\) −3.69514e7 −0.991725
\(335\) 4.53938e7i 1.20743i
\(336\) −4.66334e6 + 1.58770e6i −0.122936 + 0.0418553i
\(337\) 3.43359e7 0.897137 0.448568 0.893748i \(-0.351934\pi\)
0.448568 + 0.893748i \(0.351934\pi\)
\(338\) 1.91982e7i 0.497176i
\(339\) −1.13671e7 3.33871e7i −0.291777 0.856999i
\(340\) −2.51953e7 −0.641038
\(341\) 3.61353e7i 0.911316i
\(342\) −2.46955e7 3.20634e7i −0.617361 0.801552i
\(343\) 2.17889e6 0.0539949
\(344\) 7.48294e7i 1.83822i
\(345\) 5.68200e7 1.93452e7i 1.38371 0.471102i
\(346\) −4.84010e7 −1.16849
\(347\) 5.43933e7i 1.30184i 0.759147 + 0.650919i \(0.225616\pi\)
−0.759147 + 0.650919i \(0.774384\pi\)
\(348\) −4.29520e6 1.26157e7i −0.101917 0.299347i
\(349\) −9.96472e6 −0.234417 −0.117208 0.993107i \(-0.537395\pi\)
−0.117208 + 0.993107i \(0.537395\pi\)
\(350\) 4.04278e6i 0.0942921i
\(351\) −1.37107e7 + 2.06407e7i −0.317059 + 0.477312i
\(352\) −4.73820e7 −1.08639
\(353\) 7.31427e7i 1.66283i 0.555656 + 0.831413i \(0.312467\pi\)
−0.555656 + 0.831413i \(0.687533\pi\)
\(354\) −2.74100e7 + 9.33211e6i −0.617873 + 0.210363i
\(355\) −6.33326e7 −1.41560
\(356\) 2.38447e7i 0.528497i
\(357\) −6.79728e6 1.99648e7i −0.149393 0.438793i
\(358\) 4.20507e7 0.916483
\(359\) 1.99515e7i 0.431213i −0.976480 0.215607i \(-0.930827\pi\)
0.976480 0.215607i \(-0.0691729\pi\)
\(360\) 4.59399e7 3.53832e7i 0.984652 0.758386i
\(361\) 4.08407e7 0.868104
\(362\) 4.09932e7i 0.864143i
\(363\) −3.40975e7 + 1.16090e7i −0.712857 + 0.242702i
\(364\) −4.72189e6 −0.0979066
\(365\) 7.21031e6i 0.148277i
\(366\) 1.54950e7 + 4.55116e7i 0.316046 + 0.928279i
\(367\) 1.97764e6 0.0400082 0.0200041 0.999800i \(-0.493632\pi\)
0.0200041 + 0.999800i \(0.493632\pi\)
\(368\) 2.16461e7i 0.434345i
\(369\) 2.61744e7 + 3.39836e7i 0.520952 + 0.676380i
\(370\) 7.24849e6 0.143101
\(371\) 1.63076e7i 0.319350i
\(372\) −1.51627e7 + 5.16235e6i −0.294542 + 0.100281i
\(373\) 2.62130e7 0.505114 0.252557 0.967582i \(-0.418728\pi\)
0.252557 + 0.967582i \(0.418728\pi\)
\(374\) 6.28787e7i 1.20196i
\(375\) −1.30292e7 3.82690e7i −0.247073 0.725694i
\(376\) −1.54429e7 −0.290513
\(377\) 2.14780e7i 0.400839i
\(378\) 1.25871e7 + 8.36112e6i 0.233051 + 0.154806i
\(379\) 5.21829e7 0.958540 0.479270 0.877668i \(-0.340901\pi\)
0.479270 + 0.877668i \(0.340901\pi\)
\(380\) 3.92022e7i 0.714430i
\(381\) 6.10756e7 2.07940e7i 1.10431 0.375979i
\(382\) 3.06553e7 0.549941
\(383\) 4.08689e7i 0.727439i 0.931509 + 0.363719i \(0.118493\pi\)
−0.931509 + 0.363719i \(0.881507\pi\)
\(384\) 2.12752e6 + 6.24890e6i 0.0375734 + 0.110359i
\(385\) 3.30216e7 0.578650
\(386\) 4.73414e7i 0.823150i
\(387\) −7.85309e7 + 6.04850e7i −1.35490 + 1.04355i
\(388\) −4.13062e6 −0.0707163
\(389\) 6.03432e7i 1.02513i 0.858648 + 0.512566i \(0.171305\pi\)
−0.858648 + 0.512566i \(0.828695\pi\)
\(390\) −2.75414e7 + 9.37686e6i −0.464293 + 0.158075i
\(391\) 9.26713e7 1.55030
\(392\) 9.24936e6i 0.153551i
\(393\) −1.84427e7 5.41693e7i −0.303841 0.892434i
\(394\) −2.01337e7 −0.329180
\(395\) 7.30841e7i 1.18586i
\(396\) 2.26799e7 + 2.94465e7i 0.365221 + 0.474186i
\(397\) −2.28136e7 −0.364604 −0.182302 0.983243i \(-0.558355\pi\)
−0.182302 + 0.983243i \(0.558355\pi\)
\(398\) 4.30281e7i 0.682501i
\(399\) −3.10638e7 + 1.05761e7i −0.489030 + 0.166497i
\(400\) 7.41106e6 0.115798
\(401\) 1.73802e7i 0.269538i 0.990877 + 0.134769i \(0.0430293\pi\)
−0.990877 + 0.134769i \(0.956971\pi\)
\(402\) 1.61843e7 + 4.75362e7i 0.249125 + 0.731722i
\(403\) 2.58142e7 0.394406
\(404\) 1.89993e7i 0.288134i
\(405\) −7.42670e7 1.96119e7i −1.11797 0.295227i
\(406\) 1.30978e7 0.195713
\(407\) 1.49240e7i 0.221361i
\(408\) 8.47502e7 2.88544e7i 1.24784 0.424846i
\(409\) 3.55479e6 0.0519570 0.0259785 0.999663i \(-0.491730\pi\)
0.0259785 + 0.999663i \(0.491730\pi\)
\(410\) 5.03637e7i 0.730745i
\(411\) −9.44081e6 2.77293e7i −0.135983 0.399405i
\(412\) 2.23697e7 0.319867
\(413\) 2.34773e7i 0.333271i
\(414\) −5.26045e7 + 4.05164e7i −0.741348 + 0.570991i
\(415\) 4.93619e7 0.690634
\(416\) 3.38485e7i 0.470175i
\(417\) −1.00304e8 + 3.41498e7i −1.38328 + 0.470956i
\(418\) 9.78350e7 1.33957
\(419\) 6.97645e7i 0.948402i −0.880417 0.474201i \(-0.842737\pi\)
0.880417 0.474201i \(-0.157263\pi\)
\(420\) −4.71752e6 1.38561e7i −0.0636745 0.187023i
\(421\) −9.88875e7 −1.32524 −0.662621 0.748955i \(-0.730556\pi\)
−0.662621 + 0.748955i \(0.730556\pi\)
\(422\) 1.04035e8i 1.38434i
\(423\) 1.24826e7 + 1.62068e7i 0.164924 + 0.214130i
\(424\) 6.92254e7 0.908171
\(425\) 3.17283e7i 0.413314i
\(426\) 6.63216e7 2.25801e7i 0.857879 0.292077i
\(427\) 3.89816e7 0.500699
\(428\) 4.20527e7i 0.536367i
\(429\) −1.93061e7 5.67052e7i −0.244524 0.718209i
\(430\) −1.16383e8 −1.46381
\(431\) 6.40790e7i 0.800358i −0.916437 0.400179i \(-0.868948\pi\)
0.916437 0.400179i \(-0.131052\pi\)
\(432\) −1.53273e7 + 2.30742e7i −0.190114 + 0.286204i
\(433\) −5.28195e7 −0.650624 −0.325312 0.945607i \(-0.605469\pi\)
−0.325312 + 0.945607i \(0.605469\pi\)
\(434\) 1.57421e7i 0.192572i
\(435\) −6.30262e7 + 2.14581e7i −0.765690 + 0.260690i
\(436\) −1.27022e7 −0.153256
\(437\) 1.44190e8i 1.72779i
\(438\) 2.57071e6 + 7.55061e6i 0.0305936 + 0.0898586i
\(439\) 4.94450e7 0.584425 0.292212 0.956353i \(-0.405609\pi\)
0.292212 + 0.956353i \(0.405609\pi\)
\(440\) 1.40176e8i 1.64557i
\(441\) 9.70689e6 7.47631e6i 0.113179 0.0871709i
\(442\) −4.49190e7 −0.520192
\(443\) 1.12773e8i 1.29716i 0.761146 + 0.648581i \(0.224637\pi\)
−0.761146 + 0.648581i \(0.775363\pi\)
\(444\) 6.26222e6 2.13206e6i 0.0715450 0.0243585i
\(445\) −1.19124e8 −1.35183
\(446\) 1.29914e7i 0.146437i
\(447\) 1.88524e7 + 5.53728e7i 0.211079 + 0.619975i
\(448\) −3.23185e7 −0.359433
\(449\) 3.16029e7i 0.349131i 0.984646 + 0.174565i \(0.0558521\pi\)
−0.984646 + 0.174565i \(0.944148\pi\)
\(450\) −1.38718e7 1.80104e7i −0.152228 0.197646i
\(451\) −1.03694e8 −1.13038
\(452\) 3.77921e7i 0.409248i
\(453\) 1.10892e8 3.77546e7i 1.19290 0.406140i
\(454\) 7.16172e7 0.765331
\(455\) 2.35898e7i 0.250432i
\(456\) −4.48954e7 1.31865e8i −0.473486 1.39071i
\(457\) −8.46468e7 −0.886874 −0.443437 0.896305i \(-0.646241\pi\)
−0.443437 + 0.896305i \(0.646241\pi\)
\(458\) 2.58526e7i 0.269097i
\(459\) −9.87857e7 6.56193e7i −1.02154 0.678568i
\(460\) 6.43167e7 0.660770
\(461\) 1.14018e8i 1.16377i 0.813269 + 0.581887i \(0.197686\pi\)
−0.813269 + 0.581887i \(0.802314\pi\)
\(462\) −3.45801e7 + 1.17733e7i −0.350671 + 0.119391i
\(463\) 1.13239e8 1.14092 0.570458 0.821327i \(-0.306766\pi\)
0.570458 + 0.821327i \(0.306766\pi\)
\(464\) 2.40103e7i 0.240350i
\(465\) 2.57903e7 + 7.57504e7i 0.256506 + 0.753401i
\(466\) −4.13224e7 −0.408346
\(467\) 1.45343e7i 0.142706i −0.997451 0.0713530i \(-0.977268\pi\)
0.997451 0.0713530i \(-0.0227317\pi\)
\(468\) −2.10359e7 + 1.62020e7i −0.205222 + 0.158063i
\(469\) 4.07158e7 0.394679
\(470\) 2.40185e7i 0.231341i
\(471\) 1.35585e8 4.61617e7i 1.29762 0.441793i
\(472\) −9.96607e7 −0.947759
\(473\) 2.39621e8i 2.26434i
\(474\) 2.60568e7 + 7.65334e7i 0.244673 + 0.718647i
\(475\) 4.93670e7 0.460634
\(476\) 2.25989e7i 0.209539i
\(477\) −5.59552e7 7.26497e7i −0.515568 0.669389i
\(478\) 7.76172e7 0.710680
\(479\) 1.15987e8i 1.05536i 0.849442 + 0.527681i \(0.176939\pi\)
−0.849442 + 0.527681i \(0.823061\pi\)
\(480\) 9.93268e7 3.38172e7i 0.898137 0.305783i
\(481\) −1.06613e7 −0.0958021
\(482\) 3.20741e7i 0.286427i
\(483\) 1.73516e7 + 5.09645e7i 0.153992 + 0.452300i
\(484\) −3.85962e7 −0.340415
\(485\) 2.06359e7i 0.180883i
\(486\) 8.47644e7 5.94105e6i 0.738422 0.0517553i
\(487\) 5.67850e7 0.491639 0.245820 0.969316i \(-0.420943\pi\)
0.245820 + 0.969316i \(0.420943\pi\)
\(488\) 1.65477e8i 1.42389i
\(489\) 1.17232e8 3.99132e7i 1.00258 0.341342i
\(490\) 1.43856e7 0.122276
\(491\) 1.15095e7i 0.0972326i −0.998818 0.0486163i \(-0.984519\pi\)
0.998818 0.0486163i \(-0.0154812\pi\)
\(492\) 1.48139e7 + 4.35109e7i 0.124387 + 0.365345i
\(493\) −1.02793e8 −0.857875
\(494\) 6.98909e7i 0.579749i
\(495\) 1.47110e8 1.13305e8i 1.21291 0.934188i
\(496\) 2.88577e7 0.236492
\(497\) 5.68059e7i 0.462726i
\(498\) −5.16916e7 + 1.75991e7i −0.418535 + 0.142496i
\(499\) 9.78927e7 0.787859 0.393930 0.919141i \(-0.371115\pi\)
0.393930 + 0.919141i \(0.371115\pi\)
\(500\) 4.33181e7i 0.346545i
\(501\) 5.42989e7 + 1.59485e8i 0.431795 + 1.26826i
\(502\) −1.73444e7 −0.137104
\(503\) 5.09840e7i 0.400618i −0.979733 0.200309i \(-0.935805\pi\)
0.979733 0.200309i \(-0.0641946\pi\)
\(504\) 3.17368e7 + 4.12056e7i 0.247898 + 0.321859i
\(505\) −9.49177e7 −0.737010
\(506\) 1.60512e8i 1.23896i
\(507\) −8.28608e7 + 2.82111e7i −0.635807 + 0.216469i
\(508\) 6.91337e7 0.527350
\(509\) 5.52683e7i 0.419105i −0.977797 0.209553i \(-0.932799\pi\)
0.977797 0.209553i \(-0.0672007\pi\)
\(510\) −4.48774e7 1.31813e8i −0.338312 0.993680i
\(511\) 6.46725e6 0.0484682
\(512\) 8.74079e7i 0.651239i
\(513\) −1.02099e8 + 1.53704e8i −0.756258 + 1.13850i
\(514\) 6.88852e7 0.507267
\(515\) 1.11756e8i 0.818177i
\(516\) −1.00547e8 + 3.42326e7i −0.731847 + 0.249167i
\(517\) −4.94518e7 −0.357858
\(518\) 6.50150e6i 0.0467761i
\(519\) 7.11237e7 + 2.08902e8i 0.508759 + 1.49431i
\(520\) −1.00138e8 −0.712182
\(521\) 8.63374e7i 0.610500i 0.952272 + 0.305250i \(0.0987400\pi\)
−0.952272 + 0.305250i \(0.901260\pi\)
\(522\) 5.83502e7 4.49417e7i 0.410234 0.315965i
\(523\) −1.74938e8 −1.22287 −0.611433 0.791296i \(-0.709407\pi\)
−0.611433 + 0.791296i \(0.709407\pi\)
\(524\) 6.13163e7i 0.426169i
\(525\) −1.74489e7 + 5.94073e6i −0.120584 + 0.0410546i
\(526\) −1.22519e8 −0.841871
\(527\) 1.23546e8i 0.844106i
\(528\) −2.15823e7 6.33908e7i −0.146621 0.430650i
\(529\) −8.85282e7 −0.598018
\(530\) 1.07667e8i 0.723192i
\(531\) 8.05563e7 + 1.04590e8i 0.538041 + 0.698568i
\(532\) −3.51623e7 −0.233530
\(533\) 7.40765e7i 0.489214i
\(534\) 1.24747e8 4.24717e7i 0.819229 0.278918i
\(535\) 2.10088e8 1.37196
\(536\) 1.72838e8i 1.12239i
\(537\) −6.17922e7 1.81494e8i −0.399035 1.17203i
\(538\) −1.72711e8 −1.10911
\(539\) 2.96186e7i 0.189146i
\(540\) −6.85603e7 4.55418e7i −0.435403 0.289220i
\(541\) −1.59466e8 −1.00711 −0.503553 0.863964i \(-0.667974\pi\)
−0.503553 + 0.863964i \(0.667974\pi\)
\(542\) 4.37465e7i 0.274755i
\(543\) −1.76930e8 + 6.02381e7i −1.10510 + 0.376246i
\(544\) 1.61998e8 1.00627
\(545\) 6.34581e7i 0.392010i
\(546\) −8.41053e6 2.47032e7i −0.0516708 0.151766i
\(547\) −7.00929e7 −0.428265 −0.214132 0.976805i \(-0.568692\pi\)
−0.214132 + 0.976805i \(0.568692\pi\)
\(548\) 3.13878e7i 0.190730i
\(549\) 1.73662e8 1.33756e8i 1.04951 0.808342i
\(550\) 5.49552e7 0.330309
\(551\) 1.59939e8i 0.956094i
\(552\) −2.16344e8 + 7.36572e7i −1.28625 + 0.437923i
\(553\) 6.55525e7 0.387627
\(554\) 1.65309e8i 0.972226i
\(555\) −1.06514e7 3.12851e7i −0.0623059 0.183003i
\(556\) −1.13538e8 −0.660564
\(557\) 1.25867e8i 0.728361i 0.931328 + 0.364180i \(0.118651\pi\)
−0.931328 + 0.364180i \(0.881349\pi\)
\(558\) −5.40149e7 7.01305e7i −0.310893 0.403649i
\(559\) 1.71179e8 0.979977
\(560\) 2.63711e7i 0.150163i
\(561\) 2.71390e8 9.23983e7i 1.53711 0.523330i
\(562\) 5.41611e7 0.305126
\(563\) 1.55535e8i 0.871569i −0.900051 0.435784i \(-0.856471\pi\)
0.900051 0.435784i \(-0.143529\pi\)
\(564\) 7.06476e6 + 2.07504e7i 0.0393786 + 0.115662i
\(565\) −1.88804e8 −1.04680
\(566\) 1.50512e8i 0.830083i
\(567\) 1.75908e7 6.66135e7i 0.0965022 0.365437i
\(568\) 2.41140e8 1.31591
\(569\) 3.14182e8i 1.70547i −0.522341 0.852737i \(-0.674941\pi\)
0.522341 0.852737i \(-0.325059\pi\)
\(570\) −2.05091e8 + 6.98262e7i −1.10745 + 0.377045i
\(571\) 4.88889e7 0.262604 0.131302 0.991342i \(-0.458084\pi\)
0.131302 + 0.991342i \(0.458084\pi\)
\(572\) 6.41867e7i 0.342970i
\(573\) −4.50470e7 1.32311e8i −0.239443 0.703285i
\(574\) −4.51735e7 −0.238863
\(575\) 8.09935e7i 0.426036i
\(576\) −1.43978e8 + 1.10893e8i −0.753406 + 0.580278i
\(577\) 2.77649e8 1.44533 0.722667 0.691197i \(-0.242916\pi\)
0.722667 + 0.691197i \(0.242916\pi\)
\(578\) 7.20419e7i 0.373080i
\(579\) −2.04329e8 + 6.95667e7i −1.05268 + 0.358398i
\(580\) −7.13417e7 −0.365645
\(581\) 4.42750e7i 0.225751i
\(582\) −7.35737e6 2.16098e7i −0.0373210 0.109618i
\(583\) 2.21675e8 1.11870
\(584\) 2.74534e7i 0.137834i
\(585\) 8.09425e7 + 1.05092e8i 0.404305 + 0.524930i
\(586\) 8.21665e7 0.408321
\(587\) 2.10445e7i 0.104046i 0.998646 + 0.0520230i \(0.0165669\pi\)
−0.998646 + 0.0520230i \(0.983433\pi\)
\(588\) 1.24282e7 4.23136e6i 0.0611331 0.0208136i
\(589\) 1.92229e8 0.940748
\(590\) 1.55003e8i 0.754717i
\(591\) 2.95858e7 + 8.68984e7i 0.143324 + 0.420968i
\(592\) −1.19183e7 −0.0574446
\(593\) 2.99569e8i 1.43659i 0.695739 + 0.718295i \(0.255077\pi\)
−0.695739 + 0.718295i \(0.744923\pi\)
\(594\) −1.13656e8 + 1.71102e8i −0.542293 + 0.816388i
\(595\) −1.12900e8 −0.535975
\(596\) 6.26786e7i 0.296060i
\(597\) −1.85713e8 + 6.32285e7i −0.872808 + 0.297159i
\(598\) 1.14666e8 0.536204
\(599\) 2.59759e8i 1.20862i 0.796748 + 0.604312i \(0.206552\pi\)
−0.796748 + 0.604312i \(0.793448\pi\)
\(600\) −2.52183e7 7.40705e7i −0.116752 0.342919i
\(601\) 7.52160e6 0.0346487 0.0173243 0.999850i \(-0.494485\pi\)
0.0173243 + 0.999850i \(0.494485\pi\)
\(602\) 1.04389e8i 0.478482i
\(603\) 1.81387e8 1.39706e8i 0.827285 0.637181i
\(604\) 1.25523e8 0.569654
\(605\) 1.92821e8i 0.870737i
\(606\) 9.93974e7 3.38412e7i 0.446640 0.152065i
\(607\) −8.22850e7 −0.367921 −0.183961 0.982934i \(-0.558892\pi\)
−0.183961 + 0.982934i \(0.558892\pi\)
\(608\) 2.52058e8i 1.12148i
\(609\) −1.92468e7 5.65311e7i −0.0852131 0.250285i
\(610\) 2.57367e8 1.13387
\(611\) 3.53271e7i 0.154876i
\(612\) −7.75423e7 1.00677e8i −0.338286 0.439215i
\(613\) −2.05993e7 −0.0894277 −0.0447138 0.999000i \(-0.514238\pi\)
−0.0447138 + 0.999000i \(0.514238\pi\)
\(614\) 1.26650e7i 0.0547141i
\(615\) 2.17374e8 7.40079e7i 0.934505 0.318165i
\(616\) −1.25731e8 −0.537896
\(617\) 2.59281e8i 1.10386i 0.833889 + 0.551932i \(0.186109\pi\)
−0.833889 + 0.551932i \(0.813891\pi\)
\(618\) 3.98445e7 + 1.17030e8i 0.168812 + 0.495829i
\(619\) 2.09715e8 0.884212 0.442106 0.896963i \(-0.354231\pi\)
0.442106 + 0.896963i \(0.354231\pi\)
\(620\) 8.57447e7i 0.359776i
\(621\) 2.52172e8 + 1.67508e8i 1.05299 + 0.699455i
\(622\) 1.30544e8 0.542481
\(623\) 1.06848e8i 0.441879i
\(624\) 4.52848e7 1.54179e7i 0.186380 0.0634556i
\(625\) −2.98691e8 −1.22344
\(626\) 4.45746e7i 0.181704i
\(627\) −1.43765e8 4.22263e8i −0.583246 1.71309i
\(628\) 1.53473e8 0.619661
\(629\) 5.10247e7i 0.205035i
\(630\) 6.40874e7 4.93606e7i 0.256302 0.197405i
\(631\) −1.33312e8 −0.530615 −0.265308 0.964164i \(-0.585473\pi\)
−0.265308 + 0.964164i \(0.585473\pi\)
\(632\) 2.78269e8i 1.10234i
\(633\) −4.49023e8 + 1.52876e8i −1.77034 + 0.602737i
\(634\) −6.56198e7 −0.257494
\(635\) 3.45381e8i 1.34889i
\(636\) −3.16689e7 9.30169e7i −0.123101 0.361569i
\(637\) −2.11588e7 −0.0818601
\(638\) 1.78044e8i 0.685590i
\(639\) −1.94915e8 2.53068e8i −0.747038 0.969919i
\(640\) 3.53374e7 0.134801
\(641\) 3.80864e8i 1.44609i −0.690801 0.723045i \(-0.742742\pi\)
0.690801 0.723045i \(-0.257258\pi\)
\(642\) −2.20004e8 + 7.49033e7i −0.831429 + 0.283071i
\(643\) −3.98844e8 −1.50027 −0.750136 0.661284i \(-0.770012\pi\)
−0.750136 + 0.661284i \(0.770012\pi\)
\(644\) 5.76886e7i 0.215989i
\(645\) 1.71021e8 + 5.02317e8i 0.637338 + 1.87197i
\(646\) −3.34496e8 −1.24078
\(647\) 2.61564e8i 0.965752i −0.875689 0.482876i \(-0.839592\pi\)
0.875689 0.482876i \(-0.160408\pi\)
\(648\) 2.82773e8 + 7.46729e7i 1.03923 + 0.274434i
\(649\) −3.19136e8 −1.16746
\(650\) 3.92586e7i 0.142954i
\(651\) −6.79440e7 + 2.31325e7i −0.246268 + 0.0838454i
\(652\) 1.32699e8 0.478768
\(653\) 5.21308e8i 1.87221i −0.351718 0.936106i \(-0.614402\pi\)
0.351718 0.936106i \(-0.385598\pi\)
\(654\) −2.26249e7 6.64530e7i −0.0808821 0.237565i
\(655\) −3.06326e8 −1.09009
\(656\) 8.28103e7i 0.293341i
\(657\) 2.88114e7 2.21907e7i 0.101594 0.0782485i
\(658\) −2.15433e7 −0.0756196
\(659\) 3.49679e8i 1.22184i −0.791694 0.610918i \(-0.790800\pi\)
0.791694 0.610918i \(-0.209200\pi\)
\(660\) 1.88353e8 6.41272e7i 0.655148 0.223054i
\(661\) 2.26886e8 0.785602 0.392801 0.919624i \(-0.371506\pi\)
0.392801 + 0.919624i \(0.371506\pi\)
\(662\) 1.86735e8i 0.643654i
\(663\) 6.60071e7 + 1.93874e8i 0.226490 + 0.665241i
\(664\) −1.87947e8 −0.641993
\(665\) 1.75665e8i 0.597338i
\(666\) 2.23083e7 + 2.89640e7i 0.0755167 + 0.0980474i
\(667\) 2.62403e8 0.884282
\(668\) 1.80527e8i 0.605638i
\(669\) 5.60718e7 1.90904e7i 0.187269 0.0637584i
\(670\) 2.68816e8 0.893780
\(671\) 5.29894e8i 1.75397i
\(672\) 3.03322e7 + 8.90907e7i 0.0999529 + 0.293579i
\(673\) −2.64148e8 −0.866565 −0.433283 0.901258i \(-0.642645\pi\)
−0.433283 + 0.901258i \(0.642645\pi\)
\(674\) 2.03333e8i 0.664091i
\(675\) −5.73504e7 + 8.63374e7i −0.186477 + 0.280729i
\(676\) −9.37933e7 −0.303621
\(677\) 3.84404e8i 1.23886i −0.785052 0.619429i \(-0.787364\pi\)
0.785052 0.619429i \(-0.212636\pi\)
\(678\) 1.97714e8 6.73146e7i 0.634379 0.215983i
\(679\) −1.85093e7 −0.0591262
\(680\) 4.79260e8i 1.52421i
\(681\) −1.05239e8 3.09105e8i −0.333224 0.978735i
\(682\) 2.13989e8 0.674587
\(683\) 5.31494e8i 1.66816i 0.551647 + 0.834078i \(0.313999\pi\)
−0.551647 + 0.834078i \(0.686001\pi\)
\(684\) −1.56647e8 + 1.20650e8i −0.489501 + 0.377017i
\(685\) −1.56808e8 −0.487863
\(686\) 1.29031e7i 0.0399689i
\(687\) 1.11582e8 3.79896e7i 0.344131 0.117164i
\(688\) 1.91362e8 0.587611
\(689\) 1.58359e8i 0.484157i
\(690\) 1.14560e8 + 3.36481e8i 0.348726 + 1.02427i
\(691\) −3.70050e8 −1.12157 −0.560784 0.827962i \(-0.689500\pi\)
−0.560784 + 0.827962i \(0.689500\pi\)
\(692\) 2.36464e8i 0.713588i
\(693\) 1.01629e8 + 1.31950e8i 0.305363 + 0.396469i
\(694\) −3.22110e8 −0.963664
\(695\) 5.67216e8i 1.68964i
\(696\) 2.39974e8 8.17023e7i 0.711764 0.242330i
\(697\) 3.54528e8 1.04701
\(698\) 5.90098e7i 0.173523i
\(699\) 6.07220e7 + 1.78351e8i 0.177793 + 0.522208i
\(700\) −1.97511e7 −0.0575834
\(701\) 2.97612e8i 0.863965i 0.901882 + 0.431982i \(0.142186\pi\)
−0.901882 + 0.431982i \(0.857814\pi\)
\(702\) −1.22231e8 8.11932e7i −0.353322 0.234698i
\(703\) −7.93910e7 −0.228510
\(704\) 4.39320e8i 1.25911i
\(705\) 1.03666e8 3.52944e7i 0.295847 0.100725i
\(706\) −4.33141e8 −1.23088
\(707\) 8.51360e7i 0.240910i
\(708\) 4.55923e7 + 1.33912e8i 0.128467 + 0.377330i
\(709\) 3.42752e8 0.961704 0.480852 0.876802i \(-0.340328\pi\)
0.480852 + 0.876802i \(0.340328\pi\)
\(710\) 3.75047e8i 1.04788i
\(711\) 2.92034e8 2.24927e8i 0.812503 0.625795i
\(712\) 4.53569e8 1.25662
\(713\) 3.15379e8i 0.870089i
\(714\) 1.18229e8 4.02526e7i 0.324809 0.110586i
\(715\) −3.20666e8 −0.877274
\(716\) 2.05440e8i 0.559688i
\(717\) −1.14056e8 3.35002e8i −0.309429 0.908845i
\(718\) 1.18150e8 0.319199
\(719\) 1.85318e8i 0.498576i −0.968429 0.249288i \(-0.919803\pi\)
0.968429 0.249288i \(-0.0801966\pi\)
\(720\) 9.04858e7 + 1.17483e8i 0.242428 + 0.314757i
\(721\) 1.00239e8 0.267442
\(722\) 2.41853e8i 0.642600i
\(723\) 1.38434e8 4.71319e7i 0.366293 0.124710i
\(724\) −2.00273e8 −0.527724
\(725\) 8.98400e7i 0.235752i
\(726\) −6.87467e7 2.01921e8i −0.179656 0.527681i
\(727\) 4.21828e8 1.09782 0.548912 0.835880i \(-0.315042\pi\)
0.548912 + 0.835880i \(0.315042\pi\)
\(728\) 8.98188e7i 0.232795i
\(729\) −1.50201e8 3.57120e8i −0.387694 0.921788i
\(730\) 4.26985e7 0.109760
\(731\) 8.19260e8i 2.09734i
\(732\) 2.22348e8 7.57015e7i 0.566892 0.193006i
\(733\) 3.71133e8 0.942362 0.471181 0.882036i \(-0.343828\pi\)
0.471181 + 0.882036i \(0.343828\pi\)
\(734\) 1.17113e7i 0.0296154i
\(735\) −2.11392e7 6.20894e7i −0.0532385 0.156371i
\(736\) −4.13536e8 −1.03724
\(737\) 5.53467e8i 1.38258i
\(738\) −2.01247e8 + 1.55001e8i −0.500679 + 0.385626i
\(739\) −6.21470e8 −1.53988 −0.769940 0.638116i \(-0.779714\pi\)
−0.769940 + 0.638116i \(0.779714\pi\)
\(740\) 3.54127e7i 0.0873904i
\(741\) 3.01655e8 1.02702e8i 0.741405 0.252421i
\(742\) 9.65712e7 0.236394
\(743\) 7.90305e7i 0.192676i −0.995349 0.0963382i \(-0.969287\pi\)
0.995349 0.0963382i \(-0.0307130\pi\)
\(744\) −9.81971e7 2.88422e8i −0.238440 0.700340i
\(745\) 3.13132e8 0.757284
\(746\) 1.55230e8i 0.373903i
\(747\) 1.51918e8 + 1.97244e8i 0.364459 + 0.473196i
\(748\) 3.07196e8 0.734025
\(749\) 1.88438e8i 0.448459i
\(750\) 2.26624e8 7.71573e7i 0.537183 0.182891i
\(751\) 7.00643e8 1.65416 0.827079 0.562086i \(-0.190001\pi\)
0.827079 + 0.562086i \(0.190001\pi\)
\(752\) 3.94923e7i 0.0928665i
\(753\) 2.54871e7 + 7.48599e7i 0.0596946 + 0.175333i
\(754\) −1.27190e8 −0.296715
\(755\) 6.27091e8i 1.45710i
\(756\) 4.08485e7 6.14948e7i 0.0945389 0.142322i
\(757\) −2.45843e8 −0.566722 −0.283361 0.959013i \(-0.591449\pi\)
−0.283361 + 0.959013i \(0.591449\pi\)
\(758\) 3.09020e8i 0.709544i
\(759\) −6.92782e8 + 2.35867e8i −1.58442 + 0.539439i
\(760\) −7.45696e8 −1.69872
\(761\) 1.11614e8i 0.253258i 0.991950 + 0.126629i \(0.0404158\pi\)
−0.991950 + 0.126629i \(0.959584\pi\)
\(762\) 1.23139e8 + 3.61681e8i 0.278312 + 0.817450i
\(763\) −5.69184e7 −0.128138
\(764\) 1.49767e8i 0.335844i
\(765\) −5.02968e8 + 3.87389e8i −1.12345 + 0.865292i
\(766\) −2.42020e8 −0.538475
\(767\) 2.27983e8i 0.505262i
\(768\) −4.44793e8 + 1.51436e8i −0.981917 + 0.334307i
\(769\) 1.31906e8 0.290059 0.145030 0.989427i \(-0.453672\pi\)
0.145030 + 0.989427i \(0.453672\pi\)
\(770\) 1.95550e8i 0.428336i
\(771\) −1.01225e8 2.97314e8i −0.220863 0.648713i
\(772\) −2.31288e8 −0.502691
\(773\) 5.26599e8i 1.14010i −0.821611 0.570048i \(-0.806924\pi\)
0.821611 0.570048i \(-0.193076\pi\)
\(774\) −3.58184e8 4.65050e8i −0.772474 1.00294i
\(775\) 1.07978e8 0.231968
\(776\) 7.85717e7i 0.168144i
\(777\) 2.80610e7 9.55375e6i 0.0598191 0.0203662i
\(778\) −3.57345e8 −0.758837
\(779\) 5.51621e8i 1.16689i
\(780\) 4.58109e7 + 1.34554e8i 0.0965350 + 0.283540i
\(781\) 7.72186e8 1.62095
\(782\) 5.48788e8i 1.14758i
\(783\) −2.79716e8 1.85804e8i −0.582682 0.387052i
\(784\) −2.36535e7 −0.0490847
\(785\) 7.66729e8i 1.58501i
\(786\) 3.20784e8 1.09215e8i 0.660609 0.224914i
\(787\) −2.05228e8 −0.421029 −0.210515 0.977591i \(-0.567514\pi\)
−0.210515 + 0.977591i \(0.567514\pi\)
\(788\) 9.83635e7i 0.201028i
\(789\) 1.80037e8 + 5.28801e8i 0.366549 + 1.07662i
\(790\) 4.32795e8 0.877810
\(791\) 1.69347e8i 0.342174i
\(792\) −5.60126e8 + 4.31412e8i −1.12748 + 0.868395i
\(793\) −3.78543e8 −0.759095
\(794\) 1.35099e8i 0.269892i
\(795\) −4.64698e8 + 1.58213e8i −0.924846 + 0.314876i
\(796\) −2.10215e8 −0.416797
\(797\) 5.91897e8i 1.16915i 0.811339 + 0.584576i \(0.198739\pi\)
−0.811339 + 0.584576i \(0.801261\pi\)
\(798\) −6.26303e7 1.83956e8i −0.123247 0.361997i
\(799\) 1.69075e8 0.331466
\(800\) 1.41584e8i 0.276532i
\(801\) −3.66622e8 4.76005e8i −0.713381 0.926220i
\(802\) −1.02923e8 −0.199521
\(803\) 8.79121e7i 0.169786i
\(804\) 2.32239e8 7.90691e7i 0.446856 0.152138i
\(805\) 2.88203e8 0.552473
\(806\) 1.52868e8i 0.291952i
\(807\) 2.53794e8 + 7.45435e8i 0.482903 + 1.41837i
\(808\) 3.61401e8 0.685103
\(809\) 4.63734e8i 0.875837i 0.899015 + 0.437919i \(0.144284\pi\)
−0.899015 + 0.437919i \(0.855716\pi\)
\(810\) 1.16139e8 4.39800e8i 0.218537 0.827561i
\(811\) −2.00773e8 −0.376395 −0.188197 0.982131i \(-0.560264\pi\)
−0.188197 + 0.982131i \(0.560264\pi\)
\(812\) 6.39896e7i 0.119520i
\(813\) −1.88813e8 + 6.42841e7i −0.351367 + 0.119628i
\(814\) −8.83777e7 −0.163859
\(815\) 6.62944e8i 1.22463i
\(816\) 7.37895e7 + 2.16732e8i 0.135808 + 0.398890i
\(817\) 1.27471e9 2.33747
\(818\) 2.10510e7i 0.0384603i
\(819\) −9.42617e7 + 7.26010e7i −0.171587 + 0.132157i
\(820\) 2.46053e8 0.446260
\(821\) 3.61647e8i 0.653515i −0.945108 0.326758i \(-0.894044\pi\)
0.945108 0.326758i \(-0.105956\pi\)
\(822\) 1.64209e8 5.59073e7i 0.295653 0.100659i
\(823\) −2.84708e8 −0.510740 −0.255370 0.966843i \(-0.582197\pi\)
−0.255370 + 0.966843i \(0.582197\pi\)
\(824\) 4.25512e8i 0.760554i
\(825\) −8.07549e7 2.37191e8i −0.143816 0.422412i
\(826\) −1.39029e8 −0.246698
\(827\) 3.63770e7i 0.0643147i 0.999483 + 0.0321574i \(0.0102378\pi\)
−0.999483 + 0.0321574i \(0.989762\pi\)
\(828\) 1.97944e8 + 2.57001e8i 0.348699 + 0.452735i
\(829\) 2.91940e8 0.512425 0.256212 0.966621i \(-0.417525\pi\)
0.256212 + 0.966621i \(0.417525\pi\)
\(830\) 2.92315e8i 0.511230i
\(831\) 7.13486e8 2.42916e8i 1.24332 0.423305i
\(832\) 3.13839e8 0.544925
\(833\) 1.01265e8i 0.175197i
\(834\) −2.02231e8 5.93986e8i −0.348617 1.02395i
\(835\) 9.01884e8 1.54914
\(836\) 4.77976e8i 0.818063i
\(837\) −2.23315e8 + 3.36187e8i −0.380840 + 0.573330i
\(838\) 4.13136e8 0.702039
\(839\) 4.25640e7i 0.0720703i 0.999351 + 0.0360351i \(0.0114728\pi\)
−0.999351 + 0.0360351i \(0.988527\pi\)
\(840\) 2.63569e8 8.97356e7i 0.444689 0.151400i
\(841\) 3.03760e8 0.510672
\(842\) 5.85599e8i 0.980989i
\(843\) −7.95881e7 2.33764e8i −0.132851 0.390206i
\(844\) −5.08265e8 −0.845402
\(845\) 4.68576e8i 0.776623i
\(846\) −9.59747e7 + 7.39203e7i −0.158506 + 0.122082i
\(847\) −1.72950e8 −0.284622
\(848\) 1.77030e8i 0.290309i
\(849\) −6.49621e8 + 2.21172e8i −1.06154 + 0.361416i
\(850\) −1.87891e8 −0.305949
\(851\) 1.30252e8i 0.211347i
\(852\) −1.10316e8 3.24016e8i −0.178369 0.523899i
\(853\) −2.80622e8 −0.452142 −0.226071 0.974111i \(-0.572588\pi\)
−0.226071 + 0.974111i \(0.572588\pi\)
\(854\) 2.30844e8i 0.370634i
\(855\) 6.02750e8 + 7.82583e8i 0.964360 + 1.25208i
\(856\) −7.99917e8 −1.27533
\(857\) 9.46806e8i 1.50424i 0.659023 + 0.752122i \(0.270970\pi\)
−0.659023 + 0.752122i \(0.729030\pi\)
\(858\) 3.35801e8 1.14328e8i 0.531642 0.181005i
\(859\) −9.74495e8 −1.53745 −0.768724 0.639581i \(-0.779108\pi\)
−0.768724 + 0.639581i \(0.779108\pi\)
\(860\) 5.68591e8i 0.893933i
\(861\) 6.63810e7 + 1.94972e8i 0.104000 + 0.305466i
\(862\) 3.79468e8 0.592452
\(863\) 6.87704e8i 1.06996i −0.844864 0.534982i \(-0.820318\pi\)
0.844864 0.534982i \(-0.179682\pi\)
\(864\) 4.40821e8 + 2.92819e8i 0.683473 + 0.454003i
\(865\) 1.18134e9 1.82526
\(866\) 3.12790e8i 0.481614i
\(867\) −3.10938e8 + 1.05863e8i −0.477108 + 0.162438i
\(868\) −7.69083e7 −0.117602
\(869\) 8.91083e8i 1.35787i
\(870\) −1.27072e8 3.73233e8i −0.192971 0.566790i
\(871\) −3.95383e8 −0.598361
\(872\) 2.41618e8i 0.364401i
\(873\) −8.24583e7 + 6.35099e7i −0.123934 + 0.0954550i
\(874\) 8.53875e8 1.27897
\(875\) 1.94108e8i 0.289748i
\(876\) 3.68887e7 1.25593e7i 0.0548758 0.0186832i
\(877\) −1.03427e8 −0.153333 −0.0766667 0.997057i \(-0.524428\pi\)
−0.0766667 + 0.997057i \(0.524428\pi\)
\(878\) 2.92807e8i 0.432611i
\(879\) −1.20741e8 3.54637e8i −0.177782 0.522177i
\(880\) −3.58474e8 −0.526029
\(881\) 8.22218e8i 1.20243i −0.799088 0.601214i \(-0.794684\pi\)
0.799088 0.601214i \(-0.205316\pi\)
\(882\) 4.42737e7 + 5.74829e7i 0.0645268 + 0.0837786i
\(883\) −1.21358e9 −1.76273 −0.881365 0.472436i \(-0.843375\pi\)
−0.881365 + 0.472436i \(0.843375\pi\)
\(884\) 2.19453e8i 0.317676i
\(885\) 6.69005e8 2.27772e8i 0.965160 0.328602i
\(886\) −6.67827e8 −0.960203
\(887\) 1.73496e8i 0.248610i −0.992244 0.124305i \(-0.960330\pi\)
0.992244 0.124305i \(-0.0396701\pi\)
\(888\) 4.05556e7 + 1.19119e8i 0.0579177 + 0.170114i
\(889\) 3.09788e8 0.440919
\(890\) 7.05440e8i 1.00067i
\(891\) 9.05505e8 + 2.39120e8i 1.28014 + 0.338051i
\(892\) 6.34698e7 0.0894278
\(893\) 2.63069e8i 0.369415i
\(894\) −3.27911e8 + 1.11642e8i −0.458926 + 0.156248i
\(895\) −1.02635e9 −1.43161
\(896\) 3.16957e7i 0.0440632i
\(897\) −1.68498e8 4.94906e8i −0.233462 0.685718i
\(898\) −1.87148e8 −0.258439
\(899\) 3.49826e8i 0.481474i
\(900\) −8.79905e7 + 6.77709e7i −0.120700 + 0.0929642i
\(901\) −7.57905e8 −1.03619
\(902\) 6.14063e8i 0.836745i
\(903\) −4.50551e8 + 1.53396e8i −0.611900 + 0.208330i
\(904\) 7.18874e8 0.973078
\(905\) 1.00053e9i 1.34985i
\(906\) 2.23578e8 + 6.56687e8i 0.300639 + 0.883026i
\(907\) 1.29528e9 1.73596 0.867982 0.496595i \(-0.165416\pi\)
0.867982 + 0.496595i \(0.165416\pi\)
\(908\) 3.49888e8i 0.467381i
\(909\) −2.92123e8 3.79278e8i −0.388932 0.504971i
\(910\) −1.39696e8 −0.185378
\(911\) 1.89887e8i 0.251153i 0.992084 + 0.125577i \(0.0400781\pi\)
−0.992084 + 0.125577i \(0.959922\pi\)
\(912\) 3.37220e8 1.14811e8i 0.444559 0.151356i
\(913\) −6.01848e8 −0.790815
\(914\) 5.01268e8i 0.656494i
\(915\) −3.78193e8 1.11082e9i −0.493685 1.45004i
\(916\) 1.26304e8 0.164335
\(917\) 2.74758e8i 0.356322i
\(918\) 3.88589e8 5.84996e8i 0.502299 0.756180i
\(919\) −9.32821e8 −1.20185 −0.600927 0.799304i \(-0.705202\pi\)
−0.600927 + 0.799304i \(0.705202\pi\)
\(920\) 1.22342e9i 1.57113i
\(921\) −5.46630e7 + 1.86108e7i −0.0699705 + 0.0238224i
\(922\) −6.75197e8 −0.861465
\(923\) 5.51631e8i 0.701526i
\(924\) 5.75186e7 + 1.68942e8i 0.0729109 + 0.214152i
\(925\) −4.45949e7 −0.0563456
\(926\) 6.70587e8i 0.844544i
\(927\) 4.46560e8 3.43944e8i 0.560584 0.431766i
\(928\) 4.58705e8 0.573970
\(929\) 8.77845e7i 0.109489i 0.998500 + 0.0547445i \(0.0174344\pi\)
−0.998500 + 0.0547445i \(0.982566\pi\)
\(930\) −4.48584e8 + 1.52727e8i −0.557693 + 0.189874i
\(931\) −1.57562e8 −0.195255
\(932\) 2.01882e8i 0.249373i
\(933\) −1.91830e8 5.63436e8i −0.236195 0.693745i
\(934\) 8.60700e7 0.105636
\(935\) 1.53470e9i 1.87754i
\(936\) −3.08190e8 4.00140e8i −0.375830 0.487960i
\(937\) −8.62672e8 −1.04864 −0.524320 0.851521i \(-0.675681\pi\)
−0.524320 + 0.851521i \(0.675681\pi\)
\(938\) 2.41113e8i 0.292155i
\(939\) 1.92387e8 6.55009e7i 0.232370 0.0791135i
\(940\) 1.17343e8 0.141278
\(941\) 1.30884e9i 1.57079i −0.618998 0.785393i \(-0.712461\pi\)
0.618998 0.785393i \(-0.287539\pi\)
\(942\) 2.73364e8 + 8.02916e8i 0.327030 + 0.960544i
\(943\) −9.05012e8 −1.07924
\(944\) 2.54863e8i 0.302964i
\(945\) −3.07218e8 2.04073e8i −0.364042 0.241818i
\(946\) 1.41900e9 1.67614
\(947\) 8.66006e8i 1.01970i 0.860264 + 0.509848i \(0.170298\pi\)
−0.860264 + 0.509848i \(0.829702\pi\)
\(948\) 3.73906e8 1.27301e8i 0.438871 0.149420i
\(949\) −6.28023e7 −0.0734813
\(950\) 2.92345e8i 0.340977i
\(951\) 9.64262e7 + 2.83220e8i 0.112112 + 0.329293i
\(952\) 4.29871e8 0.498227
\(953\) 2.34543e8i 0.270984i 0.990778 + 0.135492i \(0.0432615\pi\)
−0.990778 + 0.135492i \(0.956738\pi\)
\(954\) 4.30222e8 3.31360e8i 0.495504 0.381640i
\(955\) −7.48215e8 −0.859045
\(956\) 3.79201e8i 0.434006i
\(957\) 7.68451e8 2.61630e8i 0.876759 0.298505i
\(958\) −6.86858e8 −0.781215
\(959\) 1.40649e8i 0.159470i
\(960\) 3.13548e8 + 9.20945e8i 0.354398 + 1.04093i
\(961\) −4.67052e8 −0.526254
\(962\) 6.31348e7i 0.0709159i
\(963\) 6.46577e8 + 8.39486e8i 0.724005 + 0.940014i
\(964\) 1.56699e8 0.174918
\(965\) 1.15548e9i 1.28582i
\(966\) −3.01805e8 + 1.02754e8i −0.334807 + 0.113990i
\(967\) 1.11442e9 1.23245 0.616225 0.787570i \(-0.288661\pi\)
0.616225 + 0.787570i \(0.288661\pi\)
\(968\) 7.34169e8i 0.809412i
\(969\) 4.91532e8 + 1.44371e9i 0.540232 + 1.58675i
\(970\) −1.22203e8 −0.133896
\(971\) 2.30673e8i 0.251964i 0.992033 + 0.125982i \(0.0402081\pi\)
−0.992033 + 0.125982i \(0.959792\pi\)
\(972\) −2.90252e7 4.14119e8i −0.0316065 0.450948i
\(973\) −5.08762e8 −0.552301
\(974\) 3.36273e8i 0.363928i
\(975\) 1.69443e8 5.76893e7i 0.182814 0.0622417i
\(976\) −4.23174e8 −0.455166
\(977\) 6.28575e8i 0.674021i 0.941501 + 0.337011i \(0.109416\pi\)
−0.941501 + 0.337011i \(0.890584\pi\)
\(978\) 2.36361e8 + 6.94232e8i 0.252673 + 0.742144i
\(979\) 1.45243e9 1.54792
\(980\) 7.02813e7i 0.0746726i
\(981\) −2.53570e8 + 1.95301e8i −0.268591 + 0.206870i
\(982\) 6.81578e7 0.0719749
\(983\) 7.03769e8i 0.740917i −0.928849 0.370458i \(-0.879201\pi\)
0.928849 0.370458i \(-0.120799\pi\)
\(984\) −8.27655e8 + 2.81787e8i −0.868689 + 0.295757i
\(985\) 4.91409e8 0.514202
\(986\) 6.08729e8i 0.635028i
\(987\) 3.16572e7 + 9.29825e7i 0.0329246 + 0.0967052i
\(988\) 3.41454e8 0.354047
\(989\) 2.09134e9i 2.16190i
\(990\) 6.70979e8 + 8.71168e8i 0.691518 + 0.897834i
\(991\) 3.96582e8 0.407485 0.203743 0.979025i \(-0.434689\pi\)
0.203743 + 0.979025i \(0.434689\pi\)
\(992\) 5.51312e8i 0.564758i
\(993\) −8.05964e8 + 2.74402e8i −0.823129 + 0.280246i
\(994\) 3.36397e8 0.342526
\(995\) 1.05020e9i 1.06611i
\(996\) 8.59810e7 + 2.52541e8i 0.0870211 + 0.255596i
\(997\) 7.57185e8 0.764041 0.382020 0.924154i \(-0.375228\pi\)
0.382020 + 0.924154i \(0.375228\pi\)
\(998\) 5.79708e8i 0.583200i
\(999\) 9.22296e7 1.38846e8i 0.0925068 0.139263i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 21.7.b.a.8.8 yes 12
3.2 odd 2 inner 21.7.b.a.8.5 12
4.3 odd 2 336.7.d.a.113.4 12
7.6 odd 2 147.7.b.b.50.8 12
12.11 even 2 336.7.d.a.113.3 12
21.20 even 2 147.7.b.b.50.5 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.7.b.a.8.5 12 3.2 odd 2 inner
21.7.b.a.8.8 yes 12 1.1 even 1 trivial
147.7.b.b.50.5 12 21.20 even 2
147.7.b.b.50.8 12 7.6 odd 2
336.7.d.a.113.3 12 12.11 even 2
336.7.d.a.113.4 12 4.3 odd 2